Furthermore it will be shown that, in some regions of the parameter space, trapped misalignment will automatically source the recently proposed kinetic misalignment mechanism [1]}.
In the latter, a sizeable initial axion velocity is the source of the axion relic abundance as opposed to the conventionally assumed initial misalignment angle. The original kinetic misalignment proposal [1]} required an ad-hoc Peccei Quinn (PQ)-breaking non-renormalizable effective
operator suppressed by powers of the Planck mass, \(M_{\rm Pl}\) . In contrast, we will show that the early stage of oscillations in the \(Z_{\cal N}\)  axion framework naturally flows out into kinetic misalignment.
